Astrophysics > Instrumentation and Methods for Astrophysics

Title:
An Algorithm for Radiation Magnetohydrodynamics Based on Solving the Time-dependent Transfer Equation

Abstract: (Abridged) We describe a new algorithm for solving the coupled
frequency-integrated transfer equation and the equations of
magnetohydrodynamics when the light-crossing time is only marginally shorter
than dynamical timescales. The transfer equation is solved in the mixed frame,
including velocity dependent source terms accurate to O(v/c). An operator split
approach is used to compute the specific intensity along discrete rays, with
upwind monotonic interpolation used along each ray to update the transport
terms, and implicit methods used to compute the scattering and absorption
source terms. Conservative differencing is used for the transport terms, which
ensures the specific intensity (as well as energy and momentum) are conserved
along each ray to round-off error. The use of implicit methods for the source
terms ensures the method is stable even if the source terms are very stiff. To
couple the solution of the transfer equation to the MHD algorithms in the
Athena code, we perform direct quadrature of the specific intensity over angles
to compute the energy and momentum source terms. We present the results of a
variety of tests of the method, such as calculating the structure of a non-LTE
atmosphere, an advective diffusion test, linear wave convergence tests, and the
well-known shadow test. We use new semi-analytic solutions for radiation
modified shocks to demonstrate the ability of our algorithm to capture the
effects of an anisotropic radiation field accurately. Since the method uses
explicit differencing of the spatial operators, it shows excellent weak scaling
on parallel computers. The method is ideally suited for problems in which
characteristic velocities are non-relativistic, but still within a few percent
or more of the speed of light. The method is an intermediate step towards
algorithms for fully relativistic flows.